Bianchi cosmologies with $p$-form gauge fields

Abstract

In this paper the dynamics of free gauge fields in Bianchi type I-VII${}_h$ space-times is investigated. The general equations for a matter sector consisting of a $p$-form field strength ($p\in \{1,3\}$), a cosmological constant ($4$-form) and perfect fluid in Bianchi type I-VII${}_h$ space-times are computed using the orthonormal frame method. The number of independent components of a $p$-form in all Bianchi types I-IX are derived and, by means of the dynamical systems approach, the behaviour of such fields in Bianchi type I and V are studied. Both a local and a global analysis are performed and strong global results regarding the general behaviour are obtained. New self-similar cosmological solutions appear both in Bianchi type I and Bianchi type V, in particular, a one-parameter family of self-similar solutions,"Wonderland ($\lambda$)" appears generally in type V and in type I for $\lambda =0$. Depending on the value of the equation of state parameter other new stable solutions are also found ("The Rope" and "The Edge") containing a purely spatial field strength that rotates relative to the co-moving inertial tetrad. Using monotone functions, global results are given and the conditions under which exact solutions are (global) attractors are found.

42 pages, 6 figures, 6 tables in text. V2: minor changes, matches the version published in CQG

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Cited by in corpus (11)

• Arbitrarily coupled $p-$forms in cosmological backgrounds
• Anisotropic inflation with coupled $\mathbf{p}$-forms
• Extended FLRW Models: dynamical cancellation of cosmological anisotropies
• Balancing Anisotropic Curvature with Gauge Fields in a Class of Shear-Free Cosmological Models
• Late-Time Anisotropy Sourced by a 2-Form Field Non-Minimally Coupled to Cold Dark Matter
• Bianchi models with a free massless scalar field: invariant sets and higher symmetries
• Non-canonical 3-form dark energy
• Approaching Wonderland
• Collins in Wonderland
• Power-law Bianchi type I inflation with multiple vector fields
• Bianchi cosmologies in a Thurston-based theory of gravity